Related papers: Geometry and topology in many-body physics
Using the quantum two-body system as a familiar model, this talk will describe how entanglement can be used to select preferred observables for interrogating a physical system. The symmetries and dynamics of the quantum two-body system…
The context of this paper is the use of formal methods for topology-based geometric modelling. Topology-based geometric modelling deals with objects of various dimensions and shapes. Usually, objects are defined by a graph-based topological…
Finite metric spaces arise in many different contexts. Enormous bodies of data, scientific, commercial and others can often be viewed as large metric spaces. It turns out that the metric of graphs reveals a lot of interesting information.…
We introduce the concept of entanglement halos, a set of strongly entangled distant sites within the ground state of a quantum many-body system. Such halos emerge in star-like systems with exponentially decaying couplings, as we show using…
We propose an exact construction for atypical excited states of a class of non-integrable quantum many-body Hamiltonians in one dimension (1D), two dimensions (2D), and three dimensins (3D) that display area law entanglement entropy. These…
We consider symmetries and reduction in non-relativistic many-body quantum mechanics, with the aim of identifying physically meaningful observables in systems such as molecules and crystalline solids. To this end, we propose a unified…
Recent advances in our understanding of symmetry in quantum many-body systems offer the possibility of a generalized Landau paradigm that encompasses all equilibrium phases of matter. This is a brief and elementary review of some of these…
I describe the manifestation of the non-Euclidean geometry in the behavior of collective observables of some complex physical systems. Specifically, I consider the formation of equilibrium shapes of plants and statistics of sparse random…
Recent work shows that highly excited many-body localized eigenstates can exhibit broken symmetries and topological order, including in dimensions where such order would be forbidden in equilibrium. In this paper we extend this analysis to…
A recent surge of research in many-body quantum entanglement has uncovered intriguing properties of quantum many-body systems. A prime example is the modular commutator, which can extract a topological invariant from a single wave function.…
Dissipative phenomena manifest in multiple mechanical systems. In this dissertation, different geometric frameworks for modelling non-conservative dynamics are considered. The objective is to generalize several results from conservative…
This paper collects some characteristic aspects of the general model-building framework of the mechanics of complex bodies, that are bodies in which the material substructure influences prominently the gross behavior through interactions…
Inspired by topological data analysis techniques, we introduce persistent homology observables and apply them in a geometric analysis of the dynamics of quantum field theories. As a prototype application, we consider data from a…
Modeling the electronic and optical properties of organic semiconductors remains a challenge for theory, despite the remarkable progress achieved in the last three decades. The complexity of these systems, including structural (dis)order…
In this short article, we overview a concept of electronic toroidal multipoles, and their ordering with associated physical properties in non-magnetic and magnetic materials. The toroidal multipoles are introduced as microscopic electronic…
Geometric techniques have played an important role in the seventies, for the study of the spectrum of many-body Schr\"odinger operators. In this paper we provide a formalism which also allows to study nonlinear systems. We start by defining…
The discovery of topological phases of matter and topological boundary states had tremendous impact on condensed matter physics and photonics, where topological phases are defined via energy bands, giving rise to topological band theory.…
Fractal dimensions have been used as a quantitative measure for structure of eigenstates of quantum many-body systems, useful for comparison to random matrix theory predictions or to distinguish many-body localized systems from chaotic…
The robustness properties of bipartite entanglement in systems of N bosons distributed in M different modes are analyzed using a definition of separability based on commuting algebras of observables, a natural choice when dealing with…
This paper addresses the following main question: Do we have a theoretical understanding of entanglement applicable to a full variety of physical settings? It is clear that not only the assumption of distinguishability, but also the…